Optimal Quantum State Estimation with Use of the No-Signaling Principle

TL;DR

This paper derives the optimal quantum bit state estimation method using the no-signaling principle, showing it uniquely determines the guessing probability and applies broadly across different evaluation metrics.

Contribution

It introduces a simple derivation of optimal quantum state estimation based solely on the no-signaling principle, unifying various figures of merit.

Findings

The no-signaling principle uniquely determines the guessing probability.

Optimal estimation measurement is nearly universal across different figures of merit.

The derivation simplifies understanding of quantum state estimation limits.

Abstract

A simple derivation of the optimal state estimation of a quantum bit was obtained by using the no-signaling principle. In particular, the no-signaling principle determines a unique form of the guessing probability independently of figures of merit, such as the fidelity or information gain. This proves that the optimal estimation for a quantum bit can be achieved by the same measurement for almost all figures of merit.